II A 11 B U R S 459 the sea-level; and a breakwater lias to stop their onward motion within a given space or else to change the direction of their movement. There are two ways in which this work can be performed. One is by means of a plumb wall to alter the direction of the moving water by causing it to ascend vertically, and then to allow it to descend vertically, by which process the waves are reflected and sent back seawards. Another mode is to arrest the undulations by a sloping wall of length sufficient to allow the mass of elevated water to fall down upon the slope. If, however, the slope is not long enough to enable the waves to destroy themselves, they will, though reduced in height, pursue their original direction and pass over the top of the breakwater. In this case the breakwater does not do its full amount of work, and imperfect shelter is obtained. The principle asserted in favour of the vertical wall is that oceanic waves in deep water are purely oscillatory, and exert no impact against vertical barriers, which are therefore the most eligible, as they have only to encounter the hydrostatic pressure due to the height of the impinging billows which are reflected without breaking. From the effect of winds and tide-currents already re ferred to, and perhaps from other causes, the action of which seems to have been overlooked by the advocates of the upright wall, we have good reason for believing that any form of barrier, in whatever depth of water it may be placed, must occasionally be subjected to heavy impact. The possibility of waves of translation being generated in the deepest water is. established by the following facts: first, that oceanic waves break, partially at least, long before they reach the shore, because (as admitted by the advocates of the purely oscillatory character of oceanic undulations) the depth of water is too small to admit of their being fully pro pagated ; secondly, that waves in strong tideways break in deep water during calm weather a phenomenon which is apparent to the eye and familiar to all sailors ; thirdly, and negatively, that to leeward of those races which produce broken water, and which certainly do not reflect the incom ing waves, there is comparatively smooth water both at sea and on the adjoining shore until the strength of the tide is exhausted and the race has disappeared, after which violent action is again fully manifested on the shore. Even a vertical wall, if built of ordinary masonry in courses, must during its formation present to the action of the waves at its unfinished end a sloping or at least a stepped face like a talus wall, but which, unfortunately for its stability, possesses none of the advantages of such a finished work. In short, during the most critical period of the history of every built vertical wall, the face work and heart ing are exposed, at the outer end, to the force of breaking waves. At Dunbar the force against the unfinished end of a nearly vertical wall was found by the marine dynamo meter to be nearly six times greater than on the face of the finished wall, where the waves were at the time purely oscillatory. An important advantage of the sloping wall is the small resistance which it offers to the impinging wave, but it should also be borne in mind that the weight resting on the face-stones in a talus wall is decreased in proportion to the sine of the angle of the slope. If we suppose the waves which assail a sloping wall to act in the horizontal plane, the component of their impulsive force at right angles to the surface of the talus will be proportional to the sine of the angle of inclination to the plane, while the effective force estimated in the horizontal plane will be proportional to the square of the sine of the angle of inclination. But if we assume the motion of the impinging particles to be hori zontal, the number of them which will be intercepted by the sloping surface will be also reduced in the ratio of the sine of the angle of inclination, or of the inclination of the wall to the vertical. Hence the tendency of the waves to produce horizontal displacement, on the assumption that the direction of the impinging particles is horizontal, will be pro portional to the cube of the sine of the angle of elevation of the wall. If it further happens that, owing to the relative direction of the pier and of the waves, there is an oblique action in azimuth as well as in altitude, there will be another similar reduction in the ratio of the squares or cubes of the angle of incidence, according as the component of the force is reckoned at right angles to the surface of the pier or in the direction of the waves. Let f= force of the wave on unit of surface of wall for perpen dicular incidence ; / = force on unit of surface at vertical incidence <f> and aziniuthal incidence -fy then / a/ (sin <p sin ;//) :! . , The amount of shelter which is produced by a breakwater Pro- must be measured by the length of the portion of wave tectil which is either destroyed or reflected by it. The amount va ~ u< of work done by it decreases from the maximum, which is wate at normal incidence, to zero when the waves come upon it prop "end on," in which last case it ceases to act as a breakwater tiont at all, unless to the extent due to lateral friction or erosion *^ er where there is a wall or a slope on which the end of the ^^ waves can break. come If a breakwater be so situated in relation to the coast line A br that waves may strike obliquely upon its inner or sheltered wate side, an extension of its length in the same direction will ma ^ increase the amount of sea intercepted by it. The length- ^ as ening of a breakwater may therefore, during certain winds, wave increase the sea within the harbour instead of reducing it. In such a case the extension should, if possible, be made in a dif ferent direction, or a separate breakwater may be brought from the shore so as to shelter the inner side. If these works cannot be undertaken, then an addition to the sheltered space within must be provided in which the waves can spread, or additional slopes be provided on which they can break. The table of the principal proportions of some of the most remarkable breakwaters given on p. 460 may be found useful as a guide in designing works of a similar kind. The following costs of different breakwaters are from the Cost minutes of the Institution of Civil Engineers and other breal erm rnoca W3,t6. Name of Breakwater. Depth of Water in Fathoms. Cost per Lin. Foot. Cost per Lin. Yard. Remarks. Joliette, Marseilles Marseilles (new) ... Portland 5 to 6 5 to 6 6 8 to 10 6 to 9 3 to 7 33 6-6 to 7 5 6-6 to 8-3
72 109 116 to 120 122 about 163 170 200 360
215 328 348 to 360 ( 366 480 510 600 1080 Convict labour. No rubble, all large betoii blocks. Algiers Holyhead Alderney Plymouth Dover Although some of these prices have given rise to length ened discussions as to the comparative economic advantages of the various designs, the results have not been of much value, on account of the different degrees of exposure and of depth of water at the various places. The economic values may perhaps be arrived at in a more satisfactory manner, although still but only very approximately,
thus : When x the price per foot of depth, p = the
